But others argue it's far too early to write off the newest tea-party favorite, who stunned the political world Tuesday by toppling Republican fixture and nine-term congressman Mike Castle in the party's Delaware Senate primary.

"This one may not be easy, but it's far from over," said Terry Strine, former head of the Delaware Republican Party.

Democrats cheered the O'Donnell upset, saying it all but certainly ensures that the seat, formerly held by Vice President Joe Biden, will remain in Democratic hands. Ms. O'Donnell, the Democrats believe, is too flawed a candidate to win.

Ms. O'Donnell pulled in 53% of the Republican primary vote and now faces off against Democrat Chris Coons, the executive of Delaware's dominant New Castle County, who didn't have a primary challenger. Mr. Coons has weaknesses in his own résumé to overcome—which the O'Donnell camp is aiming to exploit in the election.

Few doubt that Ms. O'Donnell faces several daunting challenges as she enters the general election. She has very little cash—just over $20,000 as of last week, compared with nearly $1 million held by the Coons campaign.

More

She is competing as a staunch conservative in a state that hasn't elected a Republican governor, senator or congressman—other than the moderate Mr. Castle—since 1994. Registered Democrats far outnumber Republicans.

The battering of the primary campaign, including a raft of ads highlighting her failure to pay nearly $12,000 in federal taxes in 2005 and her default on house payments in 2007, also appears to have tarnished her reputation among general-election voters. A Public Policy Polling survey over the weekend of 958 likely voters found that 49% saw her as "unfit to hold office," compared with 31% who deemed her fit.

But state political operatives point to factors that could tilt the race more in Ms. O'Donnell's favor.

Tuesday's turnout set a modern record for a Delaware Republican primary, with nearly a third of all registered Republicans heading to the polls—roughly four times the number in 2006. Ms. O'Donnell won not just in the conservative Sussex and Kent counties, but also in large parts of the much more populated and liberal New Castle County, which includes Wilmington and the suburbs of Philadelphia.

"Her surge in support surprised us pretty much all over the state," said one operative for the Castle campaign. "The question now is whether that surge will continue to grow."

To win in November, the O'Donnell surge will have to encompass a significant share of Delaware's 146,000 registered independents, while also siphoning off at least some support from the state's 292,000 registered Democrats. The state has 182,000 registered Republicans.

The gulf of support the 41-year-old Ms. O'Donnell needs to bridge, though, may not be as wide as many assume. She ran a distant second against Mr. Biden in 2008, but still pulled in 140,584 votes in a very big year for Democrats. That's only 30,000 votes shy of what the popular former Democratic Gov. Tom Carper tallied in winning Delaware's other Senate seat in 2006.

Republican officials also note that Mr. Coons's own vulnerabilities as a candidate haven't been vetted statewide. The 48-year-old county executive inherited a bureaucracy that was burdened with debts and unfunded obligations when he took over in 2005. Under his reign, the county council has raised property taxes three times in the last three years—by 25% last year alone.

Primary Night

Selected Race Results

Delaware GOP Senate: 100% of precincts

Christine O'Donnell: 53.1% (30,561 votes)

Michael Castle: 46.9% (27,021 votes)

Wisconsin GOP Governor: 100% of precincts (top two)

Scott Walker: 58.6% (360,053 votes)

Mark Neumann: 38.7% (237,944 votes)

New Hampshire GOP Senate: 96% of precincts (top two)

Kelly Ayotte: 38.2% (52,241 votes)

Ovide Lamontagne: 37.1% (50,839 votes)

New York Democratic House: 100% of precincts (top two)

Charlie Rangel: 50.5% (22,418 votes)

Adam Clayton Powell IV: 23.3% (10,353 votes)

"The big question is whether there will be a strong anti-incumbent sense that plays against Coons in New Castle County," said Mr. Strine, the former GOP chairman who says he considers Mr. Coons a friend. "If there is, that could spell trouble," Mr. Strine said.

Coons spokesman Daniel McElhatton said that Mr. Coons was proud of his record. "Chris has done more to reform county government in New Castle County than anyone in 25 years," he said.

In a race that has already featured plenty of mud-slinging over the candidates' past behavior, Republicans say they are likely to highlight an article that Mr. Coons wrote while in college titled "Chris Coons: The Bearded Marxist."

The article, written in 1985 when Mr. Coons was 21, describes how a semester in Kenya made him question his faith in the U.S. and the capitalist system and converted him from being a Republican to a Democrat.

Mr. McElhatton said the phrase stemmed from a Coons family joke.

After appearing to waffle Tuesday night, the National Republican Senatorial Committee said it would "strongly support" Ms. O'Donnell in the race and promised $42,000 to her campaign.

A number of national tea-party groups said they planned to provide significant help in mustering voters and running ads in the expensive Philadelphia media market. The O'Donnell campaign said it was receiving a surge of donations on Wednesday, but didn't provide details.

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